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nika2105 [10]
3 years ago
12

According to the rational root theorem what are all the potential rational roots of f(x)=9x^4-2x^2-3x+4

Mathematics
1 answer:
8_murik_8 [283]3 years ago
7 0

Answer:

+/- 1, \frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9} ....

Step-by-step explanation:

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the  leading coefficient of the function

Given: f(x)= 9x^4-2x^2-3x+4

Factors of q (leading coefficient) are: +/-9, +/-3, +/-1

Factors of p (constant term) are: +/-4 , +/-2, +/- 1

According to the theorem we write the roots in p/q form:

Therefore,

p/q =+/- 1, \frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9} ....

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Answer:

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Step-by-step explanation:

The coordinates of the turning points of the quadratic equation

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→ By comparing it with the form above

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→ Substitute x by 0 and y by -5 in the equation to find the value f c

∵ -5 = (0)² + b(0) + c

∴ -5 = 0 + 0 + c

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→ Substitute it in the equatin

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∴ 0 = 25 + 5b - 5

→ Add the like terms in the right side

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∴ -5b = 20

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∵ h = \frac{-(-4)}{2(1)} = \frac{4}{2}

∴ h = 2

→ To find k, substitute x by 2 and y by k

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∴ k = 4 - 8 - 5

∴ k = -9

∴ The cordinates of the turning point are (2, -9)

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